A duality principle for viscoelastic relaxation of cardiac muscle

Abstract

Falling cavity pressure in isovolumic relaxation of the left ventricle is analogous to isometric relaxation of force within an isolated cardiac muscle, while rising volume in early rapid filling is comparable to isotonic lengthening of the muscle fibers. Isometric relaxation and subsequent isotonic lengthening constitute the two distinct phases of physiological relaxation. With the exception of the transition between completed isometric relaxation and peak velocity of isotonic lengthening, physiological relaxation is proved equivalent to a viscoelastic behavior consisting of stress relaxation at constant strain and strain creep at constant stress. The ratio of initial (final) stress (strain) to final (initial) stress (strain) equals the ratio of initial viscoelastic material stiffness, as measured by the relaxation function, to asymptotic elastic material stiffness, as given by the shear modulus. This represents a duality principle for relaxation of cardiac muscle. The cardiac muscle is composed of material which is assumed incompressible and homogeneous with longitudinal fibers. Based on the linear theory of viscoelasticity, theoretical results are shown consistent with published observations on relaxation.